Take a look at http://www.chess.com/tactics/problems.html?sortby=rating_hard for the answer to your first two questions.
We try to add new Tactics to the database once every couple of months but this can vary.
And for your last inquiry there is not an exact feature for this but you can go to your Tactics Trainer settings page at http://www.chess.com/tactics/settings.html and then choose the "Stop only if I fail a problem". Also, on your Tactics Trainer homepage you will see "Recent Problems" under which you can click one of them to try the problem again.
How many positions are there and how high do the ratings of the positions go?
How often are positions added to the database?
Is there any way to get the tactics trainer to repeat missed positions in the future database until they are solved correctly?